Find the shortest distance from the point P = (2,2,5)

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Hint: Let $u=\langle 2,2,5\rangle$ and $v=\langle 6,5,4\rangle$, and find $\displaystyle d=\frac{|u\times v|}{|v|}$.

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Yusha
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Yusha

Updated on August 15, 2022

Comments

  • Yusha
    Yusha 2 months

    Find the shortest distance from the point $P = (2,2,5)$ to a point on the line given by $l:(x,y,z) = (-6t, -5t, -4t)$

    So I've got the matrix that I think it should look like which is

    $\begin{bmatrix}-6&-5&-4\\2&2&5\end{bmatrix}$ but what exactly am I solving here

  • Yusha
    Yusha about 6 years
    The derivative of $d(t) = 0$
  • Kaj Hansen
    Kaj Hansen about 6 years
    I'm recommending minimizing $f(t) = (d(t))^2$ by first finding $\displaystyle \frac{df}{dt}$.
  • Yusha
    Yusha about 6 years
    there is no $f$
  • Kaj Hansen
    Kaj Hansen about 6 years
    I'm just defining it to be the function $(d(t))^2$ for notational convenience.
  • Yusha
    Yusha about 6 years
    This is not a calculus class, this is linear algebra. Shouldn't have to use any sort of calculus for this
  • Kaj Hansen
    Kaj Hansen about 6 years
    That's alright; you don't have to accept my answer, and we can wait on someone else. I believe in having diverse solutions posted nevertheless.